I don't think a DR system would work due to fun factor. Sure, it's nice when taking 14 damage it's reduced to 2, but I think a player would rather not be hit at all. Combat becomes a long haul chore because it takes a lot longer to drop someone. Reducing hit points won't help because then that 2 damage starts to look a lot bigger despite not having taken 14. It becomes annoying and disheartening to keep reducing hit points 2 or 3 at a time as the combat progresses. It's slow torture. Players also will not be happy when their attack doing 15 damage gets reduced to 3 because of the monster's DR. Then of course what about spells? Do nothing then Fireball is still doing 8d6 damage while greatsword warrior is doing 4 points after DR. Include spell damage and watch spell casters master debuffing and terrain control maintaining their power. Meanwhile the warrior does 4 damage.

Maybe it is possible to create a game system that uses DR well. Ars Magica has Soak. Rollmaster has its tables where you're hit more often in heavier armor but could receive only 1 damage where in lesser armor you're hit a lot less often but when you are hit you take 30 damage where as the heavy armor wearer would have received only 10 damage on the same attack. You have to make the game system revolve around it. 5E is not wrong for not doing it this way and does not have to apologize for it.